\(\mathrm {SOT }_g\) : This one utilizes the cluster distributions to represent the substructures, and the covariance of the clusters can be understood as the difficulty of the activity for the person. Therefore, the source domain can be expressed as \(\mu _{g,s} = \sum _{i=1}^{k_s} w_{s,i} \mathcal {N}( \mathbf {z}_{s,i}, \sigma _{s,i})\)  and the target domain can be expressed as \(\mu _{g,t} = \sum _{i=1}^{k_t} w_{t,i} \mathcal {N}(\mathbf {z}_{t,i}, \sigma _{t,i})\) . The meanings of the symbols are similar to the first way. The only difference is that we use a Gaussian distribution \(\mathcal {N}(\mathbf {z},\sigma )\)  instead of a Dirac function \(\delta _\mathbf {z}\) . In this situation, the squared Wasserstein distance [1]} replaces the squared Euclidean distance as the cost function, i.e.
\(\begin{aligned}c(\mathcal {N}(\mathbf {z}_{s,i},\sigma _{s,i}), \mathcal {N}(\mathbf {z}_{t,j},\sigma _{t,j}))& = W_2^2(\mathcal {N}(\mathbf {z}_{s,i},\sigma _{s,i}), \mathcal {N}(\mathbf {z}_{t,j},\sigma _{t,j}))\\ & = ||\mathbf {z}_{s,i} - \mathbf {z}_{t,j}||^2 + B(\sigma _{s,i}, \sigma _{t,j})^2,\end{aligned}\) 
